Problem: Solve for $x$ and $y$ using substitution. ${5x-4y = -11}$ ${y = 3x+8}$
Answer: Since $y$ has already been solved for, substitute $3x+8$ for $y$ in the first equation. ${5x - 4}{(3x+8)}{= -11}$ Simplify and solve for $x$ $5x-12x - 32 = -11$ $-7x-32 = -11$ $-7x-32{+32} = -11{+32}$ $-7x = 21$ $\dfrac{-7x}{{-7}} = \dfrac{21}{{-7}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = 3x+8}\thinspace$ to find $y$ ${y = 3}{(-3)}{ + 8}$ $y = -9 + 8$ $y = -1$ You can also plug ${x = -3}$ into $\thinspace {5x-4y = -11}\thinspace$ and get the same answer for $y$ : ${5}{(-3)}{ - 4y = -11}$ ${y = -1}$